    package edu.fiu.cis.users.datastructures;

    // DisjSetsFast class
    //
    // CONSTRUCTION: with int representing initial number of sets
    //
    // ******************PUBLIC OPERATIONS*********************
    // void union( root1, root2 ) --> Merge two sets
    // int find( x )              --> Return set containing x
    // ******************ERRORS********************************
    // No error checking is performed

    /**
     * Disjoint set class, using union by rank
     * and path compression.
     * Elements in the set are numbered starting at 0.
     * @author Mark Allen Weiss
     */
    public class DisjSetsFast
    {
        /**
         * Construct the disjoint sets object.
         * @param numElements the initial number of disjoint sets.
         */
        public DisjSetsFast( int numElements )
        {
            s = new int [ numElements ];
            for( int i = 0; i < s.length; i++ )
                s[ i ] = -1;
        }

        /**
         * Union two disjoint sets using the height heuristic.
         * For simplicity, we assume root1 and root2 are distinct
         * and represent set names.
         * @param root1 the root of set 1.
         * @param root2 the root of set 2.
         */
        public void union( int root1, int root2 )
        {
            if( s[ root2 ] < s[ root1 ] )  // root2 is deeper
                s[ root1 ] = root2;        // Make root2 new root
            else
            {
                if( s[ root1 ] == s[ root2 ] )
                    s[ root1 ]--;          // Update height if same
                s[ root2 ] = root1;        // Make root1 new root
            }
        }

        /**
         * Perform a find with path compression.
         * Error checks omitted again for simplicity.
         * @param x the element being searched for.
         * @return the set containing x.
         */
        public int find( int x )
        {
            if( s[ x ] < 0 )
                return x;
            else
                return s[ x ] = find( s[ x ] );
        }

        private int [ ] s;


        // Test main; all finds on same output line should be identical
        public static void main( String [ ] args )
        {
            int NumElements = 128;
            int NumInSameSet = 16;

            DisjSetsFast ds = new DisjSetsFast( NumElements );
            int set1, set2;

            for( int k = 1; k < NumInSameSet; k *= 2 )
            {
                for( int j = 0; j + k < NumElements; j += 2 * k )
                {
                    set1 = ds.find( j );
                    set2 = ds.find( j + k );
                    ds.union( set1, set2 );
                }
            }

            for( int i = 0; i < NumElements; i++ )
            {
                System.out.print( ds.find( i )+ "*" );
                if( i % NumInSameSet == NumInSameSet - 1 )
                    System.out.println( );
            }
            System.out.println( );
        }
    }
